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  • Ising model  (3)
  • Springer  (3)
  • American Physical Society
  • Blackwell Science Ltd
  • International Union of Crystallography
  • 2000-2004
  • 1990-1994  (3)
Collection
Keywords
Publisher
  • Springer  (3)
  • American Physical Society
  • Blackwell Science Ltd
  • International Union of Crystallography
Years
Year
  • 1
    Electronic Resource
    Electronic Resource
    The Markov property method applied to Ising model calculations (1994)
    Springer
    Journal of statistical physics 77 (1994), S. 955-976 
    Details
    ISSN: 1572-9613
    Keywords: Markov property ; Ising model ; critical phenomena ; parallel computational procdures
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract An efficient method of computation for models possessing the Markov property is set out. We apply this method to the two-dimensional ising model and report exact computations for up to 10 by 10 models with periodic boundary conditions. We find that critical-point, finite-size rounding is quite large in the renormalized coupling constant, which is not divergent at the critical point, in contrast to the energy, which is also not divergent and has no rounding there. The difference is traced to the continuity of the energy and the discontinuity of the renormalized coupling constant at the critical point.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02183146
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  • 2
    Electronic Resource
    Electronic Resource
    The border model in one dimension (1990)
    Springer
    Journal of statistical physics 58 (1990), S. 467-474 
    Details
    ISSN: 1572-9613
    Keywords: Ising model ; border model ; Padé approximants ; series analysis ; universality ; pluralism ; field theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The magnetic susceptibility is studied by the methods of series analysis for the one-dimensional border model (a special case of the continuous-spin Ising model). The structure of this model is analyzed and two conjugate pairs of singularities are found near the real (physical) temperature axis. All the numerical results are consistent with the previously known rigorous results, but do not add to the knowledge of the critical properties.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01112756
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  • 3
    Electronic Resource
    Electronic Resource
    A Markov-property Monte Carlo method: One-dimensional Ising model (1993)
    Springer
    Journal of statistical physics 72 (1993), S. 621-641 
    Details
    ISSN: 1572-9613
    Keywords: Monte Carlo ; Markov property ; Ising model ; critical phenomena
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract In this paper we introduce a new Monte Carlo procedure based on the Markov property. This procedure is particularly well suited to massively parallel computation. We illustrate the method on the critical phenomena of the well known one-dimensional Ising model. In the course of this work we found that the autocorrelation time for the Metropolis Monte Carlo algorithm is closely given by the square of the correlation length. We find speedup factors of the order of 1 million for the method as implemented on the CM2 relative to a serial machine. Our procedure gives error estimates which are quite consistent with the observed deviations from the analytically known exact results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01048026
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